Abstract

We show that the field polarization of the surface-plasmon-resonance enhanced optical field can be controlled to be linear with doubled intensity enhancement by using the polarization-gated excitation scheme with two counter-incident femtosecond laser pulses under the Kretschmann configuration, which is hence used for ultrafast electron acceleration to increase the maximum kinetic energy. The spatiotemporal evolution of the polarization-gated surface-enhanced optical field is studied by means of a simplified analytical model to describe the dynamical processes of electron acceleration, the kinetic energy and emission angular distributions of the accelerated electrons.

©2009 Optical Society of America

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References

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  1. B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
    [Crossref] [PubMed]
  2. P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
    [Crossref] [PubMed]
  3. V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
    [Crossref] [PubMed]
  4. P. Baum and A. Zewail, “Attosecond electron pulses for 4D diffraction and microscopy,” Proc. Nat. Acad. Sci. 104, 18409–18414 (2007).
    [Crossref] [PubMed]
  5. M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
    [Crossref]
  6. H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
    [Crossref] [PubMed]
  7. J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
    [Crossref]
  8. J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
    [Crossref] [PubMed]
  9. S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
    [Crossref] [PubMed]
  10. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springler-Verlag, Berlin, 1988).
  11. J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
    [Crossref]
  12. P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
    [Crossref]
  13. P. Dombi and P. Rácz, “Ultrafast monoenergetic electron source by optical waveform control of surface plasmons,” Opt. Express 16, 2887–2893 (2008).
    [Crossref] [PubMed]
  14. S. Irvine and A. Elezzabi, “Surface-plasmon-based electron acceleration,” Phys. Rev. A 73, 013815 (2006).
    [Crossref]
  15. B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
    [Crossref]
  16. A. Taflove, Computational Electrodynamics (Artech House, Boston, 1995).

2008 (3)

J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
[Crossref]

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

P. Dombi and P. Rácz, “Ultrafast monoenergetic electron source by optical waveform control of surface plasmons,” Opt. Express 16, 2887–2893 (2008).
[Crossref] [PubMed]

2007 (3)

P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
[Crossref] [PubMed]

P. Baum and A. Zewail, “Attosecond electron pulses for 4D diffraction and microscopy,” Proc. Nat. Acad. Sci. 104, 18409–18414 (2007).
[Crossref] [PubMed]

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

2006 (1)

S. Irvine and A. Elezzabi, “Surface-plasmon-based electron acceleration,” Phys. Rev. A 73, 013815 (2006).
[Crossref]

2005 (1)

V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
[Crossref] [PubMed]

2004 (1)

S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
[Crossref] [PubMed]

2003 (1)

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

2002 (1)

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

2001 (2)

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
[Crossref] [PubMed]

1998 (1)

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Baskin, J.

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

Baum, P.

P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
[Crossref] [PubMed]

P. Baum and A. Zewail, “Attosecond electron pulses for 4D diffraction and microscopy,” Proc. Nat. Acad. Sci. 104, 18409–18414 (2007).
[Crossref] [PubMed]

Bryukhnevich, G.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Carey, J.

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

Dechant, A.

S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
[Crossref] [PubMed]

Dombi, P.

Dwyer, J.

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

Elezzabi, A.

S. Irvine and A. Elezzabi, “Surface-plasmon-based electron acceleration,” Phys. Rev. A 73, 013815 (2006).
[Crossref]

S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
[Crossref] [PubMed]

Irvine, S.

S. Irvine and A. Elezzabi, “Surface-plasmon-based electron acceleration,” Phys. Rev. A 73, 013815 (2006).
[Crossref]

S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
[Crossref] [PubMed]

Jaroszynski, D.

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

Jordan, R.

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

Kupersztych, J.

J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
[Crossref] [PubMed]

Kwon, O.

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

Lobastov, V.

V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
[Crossref] [PubMed]

Lozovoi, V.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Lu, P.

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

Miller, R.

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

Monastyrski, M.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Monchicourt, P.

J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
[Crossref] [PubMed]

Park, H.

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

Prokhorov, A.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Qi, H.

J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
[Crossref]

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

Rácz, P.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springler-Verlag, Berlin, 1988).

Raynaud, M.

J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
[Crossref] [PubMed]

Schelev, M.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Siwick, B.

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

Smirnov, A.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Srinivasan, R.

V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
[Crossref] [PubMed]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech House, Boston, 1995).

Vorobiev, N.

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Wu, J.

J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
[Crossref]

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

Wynne, K.

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

Yang, D.

P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
[Crossref] [PubMed]

Zawadzka, J.

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

Zeng, H.

J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
[Crossref]

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

Zewail, A.

P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
[Crossref] [PubMed]

P. Baum and A. Zewail, “Attosecond electron pulses for 4D diffraction and microscopy,” Proc. Nat. Acad. Sci. 104, 18409–18414 (2007).
[Crossref] [PubMed]

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

J. Zawadzka, D. Jaroszynski, J. Carey, and K. Wynne, “Evanescent-wave acceleration of ultrafast electron pulses,” Appl. Phys. Lett. 79, 2130–2132 (2001).
[Crossref]

J. Wu, H. Qi, and H. Zeng, “Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 051103 (2008).
[Crossref]

P. Lu, J. Wu, H. Qi, and H. Zeng, “Ponderomotive electron acceleration by polarization-gated surface-enhanced optical fields,” Appl. Phys. Lett. 93, 201108 (2008).
[Crossref]

J. Appl. Phys. (1)

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002).
[Crossref]

Nano. Lett. (1)

H. Park, J. Baskin, O. Kwon, and A. Zewail, “Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy,” Nano. Lett. 7, 2545–2551 (2007).
[Crossref] [PubMed]

Opt. Eng. (1)

M. Schelev, G. Bryukhnevich, V. Lozovoi, M. Monastyrski, A. Prokhorov, A. Smirnov, and N. Vorobiev, “500-fs photoelectron gun for time-resolved electron diffraction experiments,” Opt. Eng. 37, 2249–2254 (1998).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

S. Irvine and A. Elezzabi, “Surface-plasmon-based electron acceleration,” Phys. Rev. A 73, 013815 (2006).
[Crossref]

Phys. Rev. Lett. (2)

J. Kupersztych, P. Monchicourt, and M. Raynaud, “Ponderomotive Acceleration of Photoelectrons in Surface-Plasmon-Assisted Multiphoton Emission,” Phys. Rev. Lett. 86, 5180–5183 (2001).
[Crossref] [PubMed]

S. Irvine, A. Dechant, and A. Elezzabi, “Generation of 0.4-keV Femtosecond Electron Pulses using Impulsively Excited Surface Plasmons,” Phys. Rev. Lett. 93, 184801 (2004).
[Crossref] [PubMed]

Proc. Nat. Acad. Sci. (2)

V. Lobastov, R. Srinivasan, and A. Zewail, “Four-dimensional ultrafast electron microscopy,” Proc. Nat. Acad. Sci. 102, 7069–7073 (2005).
[Crossref] [PubMed]

P. Baum and A. Zewail, “Attosecond electron pulses for 4D diffraction and microscopy,” Proc. Nat. Acad. Sci. 104, 18409–18414 (2007).
[Crossref] [PubMed]

Science (2)

B. Siwick, J. Dwyer, R. Jordan, and R. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003).
[Crossref] [PubMed]

P. Baum, D. Yang, and A. Zewail, “4D Visualization of Transitional Structures in Phase Transformations by Electrons Diffraction,” Science 318, 788–791 (2007).
[Crossref] [PubMed]

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springler-Verlag, Berlin, 1988).

A. Taflove, Computational Electrodynamics (Artech House, Boston, 1995).

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Figures (10)

Fig. 1.
Fig. 1. Ponderomotive electron acceleration scheme based on polarization-gated SPR-enhanced optical field using the Kretschmann configuration.
Fig. 2.
Fig. 2. Time-dependent SPR-enhanced optical field components of six observation positions on the metal surface [according to Eqs. (1)] where (a) x=0, (b) x=λSP /12, (c) x=λSP /6, (d) x=λSP /4, (e) x=λSP /3, and (f) x=5λSP /12, which indicate the periodical evolution of the enhanced electric field along the metal surface. The arrows in the sub-Figs. indicate the polarization directions.
Fig. 3.
Fig. 3. (a). The polarization direction evolution of the enhanced optical field near the surface center with a period ranging from x=0 to x=λSP /2 using polarization-gated excitation scheme [according to Eqs. (1)]. Different colors stand for the different positions along the metal surface. (b). The polarization of the enhanced optical field using conventional one-pulse excitation scheme. The evolutions in (a) and (b) are observed within a time period ranged from -25 to 25 fs, where time zero indicates the envelope peak of the SPR-enhanced optical field.
Fig. 4.
Fig. 4. Superposition of the SPR-enhanced optical fields induced by incident pulse-A and pulse-B [according to Eqs. (1)] respectively at three observation positions along the metal surface of (1a) ~ (1c) x=0, (2a) ~ (2c) x=2λSP , and (3a) ~ (3c) x=-2λSP . Rows (a), (b) and (c) represent the SPR-enhanced optical fields respectively induced by incident pulse of pulse-A, pulse-B, and two synchronized pulses as shown in Fig. 1.
Fig. 5.
Fig. 5. (a) and (c) The displacement (Lx,y ) and electric field (Ex,y ) components experienced by the test electrons during the ponderomotive acceleration [according to Eqs. (1)], and (b) and (d) the velocity (Vx,y ) components of the electrons accelerated by SPR-enhanced polarization-gated excitation scheme and conventional one-pulse excitation scheme, respectively.
Fig. 6.
Fig. 6. Y-component displacements of the electrons ejected from the metal surface at different instances of an optical cycle with various phases of Ey [according to Eqs. (9) or Eqs. (14)]. Curves a, b, c, and d, respectively, represent the y-component displacements of the electrons within an optical cycle acceleration after being ejected from corresponding instances a, b, c, d as labeled in the inset.
Fig. 7.
Fig. 7. Calculated trajectories of the electrons corresponding to the excitation instances labeled in the inset [according to Eqs. (7) and Eqs. (9)], in which points 1, 5, 6, 7, and 8 stand for the instances in the same optical cycle with various phases of Ey , while points 1, 2, 3, and 4 stand for the instances in different optical cycles with same phase of Ey .
Fig. 8.
Fig. 8. (a) Polarizations of the enhanced optical fields at five observation positions along the metal surface. (b) Trajectories of electrons emitted from corresponding positions at three different instances as marked in the inset [according to Eqs. (12) and Eqs. (14)]. Line groups 1, 2, 3, 4, and 5 stand for the electrons emitted from five different positions as x=0, x=λSP /12, x=?SP/6, x=λSP /3, and x=5λSP /12, respectively. In each line group, the black, red and blue lines stand for electrons emitted from three different instances during an optical cycle as indicated in the inset of (b).
Fig. 9.
Fig. 9. Evolutions of the SPR-enhanced polarization-gated optical fields at nine observation positions along the metal surface where (a) x=-λSP /4, (b) x=-3λSP /16, (c) x=-λSP /8, (d) x=-λSP /16, (e) x=0, (f) x=λSP /16, (g) x=λSP /8, (h) x=3λSP /16, and (i) x=λSP /4 based on FDTD simulations.
Fig. 10.
Fig. 10. (a). The kinetic energy spectra and angular distributions (in the inset) of emitted electrons. The red and blue curves stand for the results by using one-pulse excitation scheme with a maximum El of 0.4×1011 V/m (ESP ~1.87×1011V/m), and polarization-gated scheme with a maximum El of 0.28×1011V/m for each incident fs laser pulse (ESP ~2.63×1011V/m), respectively. (b) and (c) respectively represent the angle-resolved kinetic energy distributions of the electrons accelerated by SPR-enhanced optical field using one-pulse excitation scheme and polarization-gated scheme, where the false color stands for the observation probability. (d) Improved emission angular distribution by coating the prism surface with a quite narrow metal film of 30 nanometers in size (based on FDTD simulations).

Equations (32)

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E SP , x _ A ( x , y , t , ) = βE ( x , t ) cos [ k SP ( x + L / 2 ) ω 0 t π / 2 + φ 0 ] e αy
E SP , y _ A ( x , y , t , ) = E ( x , t ) cos [ k SP ( x + L / 2 ) ω 0 t + φ 0 ] e αy
E SP , x _ B ( x , y , t , ) = βE ( x , t ) cos [ k SP ( x L / 2 ) ω 0 t + π / 2 + φ 0 ] e αy ,
E SP , y _ B ( x , y , t , ) = E ( x , t ) cos [ k SP ( x L / 2 ) ω 0 t + φ 0 ] e αy
E ( ± x , t ) = E 0 exp { [ ( t t 0 k SP x / ω 0 ) / τ 0 ] 2 } .
E ( x , t ) E ( x , t ) = E ( 0 , t ) = E 0 exp { [ ( t t 0 ) / τ 0 ] 2 } .
E SP , x ( 0,0 , t ) = E SP , x _ A ( 0,0 , t ) + E SP , x _ B ( 0,0 , t ) = 0
E SP , y ( 0,0 , t ) = E SP , y _ A ( 0,0 , t ) + E SP , y _ B ( 0,0 , t ) = 2 E ( 0 , t ) cos ( k SP L / 2 ω 0 t ) .
E SP , x ( x , 0 , t ) = 2 βE ( 0 , t ) sin ( k SP x ) cos ( k SP L / 2 ω 0 t )
E SP , y ( x , 0 , t ) = 2 E ( 0 , t ) cos ( k SP x ) cos ( k SP L / 2 ω 0 t )
E SP ( x , 0 , t ) = E SP , x 2 ( x , 0 , t ) + E SP , y 2 ( x , 0 , t )
= 2 E ( 0 , t ) cos ( k SP L / 2 ω 0 t ) β 2 + ( 1 β 2 ) cos 2 ( k SP x )
E x ( x , y , t ) = β E 0 sin ( ω 0 t + φ + δφ )
E y ( x , y , t ) = E 0 sin ( ω 0 t + φ ) .
E x ( x , y , t ) = β E 0 sin ( ω 0 t + φ + π / 2 )
E y ( x , y , t ) = E 0 sin ( ω 0 t + φ ) .
v x ( t ) = 0 t q E x m e dt = E 0 m e ω 0 [ sin ( ω 0 t + φ ) sin φ ]
v y ( t ) = 0 t q E y m e dt = q E 0 m e ω 0 [ cos ( ω 0 t + φ ) + cos φ ] .
L x = 0 2 π / ω 0 v x dt = 2 πqβ E 0 m e ω 0 2 sin φ
L y = 0 2 π / ω 0 v y dt = 2 πq E 0 m e ω 0 2 cos φ .
E k = 1 2 m e ( [ ( v x ) max + ( v x ) min 2 ] 2 + [ ( v y ) max + ( v y ) min 2 ] 2 )
= q 2 E 0 2 2 m e ω 0 2 [ 1 + ( β 2 1 ) sin 2 φ ] ,
tan θ = L y L x = 1 β tan φ .
E x ( x , y , t ) = ± β ( x ) E 0 sin ( ω 0 t + φ )
E y ( x , y , t ) = E 0 sin ( ω 0 t + φ ) .
v x ( t ) = 0 t q E x m e dt = ( x ) E 0 m e ω 0 [ cos ( ω 0 t + φ ) + cos φ ]
v y ( t ) = 0 t q E y m e dt = q E 0 m e ω 0 [ cos ( ω 0 t + φ ) + cos φ ] .
L x = 0 2 π / ω 0 v x dt = 2 πqβ ( x ) E 0 m e ω 0 2 cos φ
L y = 0 2 π / ω 0 v y dt = 2 πq E 0 m e ω 0 2 cos φ .
E k = 1 2 m e { [ ( v x ) max + ( v x ) min 2 ] 2 + [ ( v y ) max + ( v y ) min 2 ] 2 } ,
= [ β 2 ( x ) + 1 ] q 2 E 0 2 cos 2 φ 2 m e ω 0 2
tan θ = L y L x = ± 1 β ( x ) .

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